A PN junction device, such as a diode, is generally formed by the juxtaposing of a P type semiconductor and of an N-type semiconductor. A region where the diode operates in avalanche mode can especially be identified on the theoretical current I/voltage V characteristic of a PN junction. In this region, the diode is reverse biased with a voltage thereacross going beyond a given reverse voltage V called avalanche voltage VBK (or breakdown voltage), and the diode conducts a reverse current I which very rapidly increases. The avalanche phenomenon is generally induced for high reverse voltages (generally higher than 8 volts of reverse voltage), and the avalanche effect especially appears as a multiplication of charge carriers and the creation of a very high current.
In practice, it is possible to design PN junction diodes which, in avalanche mode, are capable of withstanding very high powers for a few tens of microseconds. Such diodes may especially be integrated in circuits as devices of protection against electrostatic discharges (ESD) which may reach several tens or even a few hundreds of volts.
Further, to decrease the time and the cost of the development cycle of an integrated circuit, simulation tools are more and more used to predict the circuit behavior in specific operating conditions. Such simulation tools generally comprise a library of mathematical models representative of the electric behavior of the components.
In particular, the electric behavior of the diode in avalanche mode may be modeled by Miller's equations:
            I      BK        =                  I        D            ·              (                  MM          -          1                )                        MM      =              1                  1          -                                    (                              V                                  V                  BK                                            )                                      m              ⁢                                                          ⁢              c                                            ,                  when        ⁢                                  ⁢        V            <              V        BK                        MM      =                        1                      1            -                          (                              1                -                ɛ                            )                                      +                                            m              ⁢                                                          ⁢              c                                      V              BK                                ·                      (                                                            (                                      1                    -                    ɛ                                    )                                                                                            m                      ⁢                                                                                          ⁢                      c                                        -                    1                                                        m                    ⁢                                                                                  ⁢                    c                                                                              1                -                                                      (                                          1                      -                      ɛ                                        )                                    2                                                      )                    ·                      (                                                            V                  BK                                ·                                                      (                                          1                      -                      ɛ                                        )                                                        1                                          m                      ⁢                                                                                          ⁢                      c                                                                                  -              V                        )                                ,  
when V≧VBK 
with                IBK: the diode current in avalanche mode,        MM: the avalanche multiplication factor,        ID: the current of the diode provided by the Shockley model,        VBK: the avalanche breakdown voltage,        V: the voltage across the diode,        mc and ε: parameters to be empirically determined.        
However, the above mathematical model does not provide a specific representation of the real behavior of the diode in avalanche mode, in particular when reverse voltage V across the diode goes beyond breakdown voltage VBK, as illustrated in FIGS. 1 and 2. In FIGS. 1 and 2, the axis of abscissas corresponds to reverse voltage V and the axis of ordinates corresponds to reverse current I in logarithmic scale. Curve C0 corresponds to the real characteristic of the diode in avalanche mode, curve C11 corresponds to the diode characteristic according to the Miller model with ε=1.e−5, and curve C12 corresponds to the diode characteristic according to the Miller model with ε=2.e−3.
As can be observed in FIGS. 1 and 2, for ε=1.e−5 (FIG. 1), the diode characteristic according to Miller's model is correctly adjusted to the portion where the amplitude of curve C0 is maximum, but is not satisfactory at the level of the substantially linear portion of curve C0. Conversely, for ε=2.e−3 (FIG. 2), the diode characteristic according to Miller's model is correctly adjusted to the substantially linear portion of curve C0, but is not satisfactory at the level of the portion where the amplitude of curve C0 is maximum.
The Miller model is thus not fully satisfactory since it does not enable to have the characteristic according to the Miller model simultaneously coincide with the real characteristic of the diode, at the level of the two portions (maximum amplitude and substantially linear portion).
Further, the Miller model is discontinuous around the breakdown voltage and thus requires a linearization around this breakdown voltage.
Another solution suggested in European Patent Application No. 2,154,619 (the disclosure of which is incorporated by reference) is to determine two currents by using a model which involves a sum of exponential type expressions. However, such solution involves a great number of parameters to be extracted. Further, as in the Miller's model, the model provided is also discontinuous around the breakdown voltage. Besides, the use of Shockley's equation for determining the reverse current, notably for reverse voltages which do not go beyond the breakdown voltage, does not allow reflecting the thermodynamic behavior of the PN junction at the breakdown point.
A more accurate mathematical model of the electric behavior of a PN junction diode is thus needed.